Robust Estimation of Skewness and Kurtosis in Distributions with Infinite Higher Moments

Abstract

This paper studies the behavior of the conventional measures of skewness and kurtosis when the data generator process is a distribution which does not possess variance or third or fourth moment and assesses the robustness of the alternative measures for these particular cases. I first show that for symmetric fat tailed distribution skewness is far from being a valid indicator of the presence of asymmetry. Secondly, I study, via Monte Carlo simulations, the behavior of the alternative measures of skewness and kurtosis when applied to distributions that do not possess finite higher moments. Finally, I present an application to the series of daily returns on a large cap US stock and show why alternative measures are a better tool to describe the distribution of financial returns.

Keywords: Skewness, Kurtosis, Fat Tails, Outliers

JEL Classification: C10, C15, C16